Pattern geomorphologic analysis for soil erosion study

Nazha Selmaoui*a,b, Isabelle Roueta, Mélanie Mahotc

aPôle Pluridisciplinaire de la Matière et de l’Environnement, EA3325 University of New-Caledonia bEquipe de Recherche en Informatique et Mathématique, EA3791 University of New-Caledonia

cENS-CACHANT, France

ABSTRACT

The geologist try to understand relationship between soil erosion observed and natural landscape structure. Erosion can effectively appears in the vicinity of linear or planar structures of soil (lines, faults or materials change). Once eroded areas are mapped, an inventory of relief linear shapes is done. The crossing geomorphological analysis with other environmental parameters allows to predict the becoming eroded areas. Lineaments detection is usually made by photo-interpretation. DEM (Digital Elevation Model) visual analysis is another alternative but not sufficient, so it uses the derived models from DEM called hillshade images. The DEM is lighted up by a virtual source with a direction and height incidence. A good study require a complete lightings visual interpretation which is very slow and subjective. This paper propose an automatic process that help geologist to detect and analyse the geomorphological structures present in the landscape by using image analysis methods. This study focus on lines and catchments basins structures. First a new watershed and catchments basins segmentation method is developed it defines an attractive structure between pixels (based on path of steepest slope). After these lines are automatically extracted by Hough transform and their preferential direction is analysed by a technique called directions rose. Some results are given on DEM and Hillshade images for a particular areas of the main New Caledonia island where soil erosion is a serious problem mainly due to tropical weather (violent rains) and human activities (mining, bush fire) on the weathered rocks (laterites) in mountain.

Keywords: image analysis, lineament, landscape segmentation, Hough transform, tropical erosion, DEM.

1. INTRODUCTION

1.1. Erosion in tropical islands context Erosion processes study in high tropical islands need a particular interest because of small geosystems and important interactions between inland, coastal region and marine life. The intense tropical erosion in these territories has a big impact on human activities and natural resources essentially in the coastal region. A consistent integrated coastal management need to consider erosion systems, their spatial and time evolution to ensure sustainable development.

Tropical island soils are often thick. They develop on very weathered rocks and all these materials (laterites, etc.) are particularly sensitive to erosion phenomena. Modelling stripped zones and understanding their dynamics are a crucial issue for tropical islands. New-Caledonia is a good example: mountains often consist in ultramafic terrains where mining activities superimpose their scars on natural tropical slopes erosion. Climatic, topographical and pedological factors are prominent in erosion processes of these terrains. Human factors like mining, deforestation or bush fires participate in erosion phenomena but it is sometimes difficult to discriminate anthropic and natural origin of erosion. Identify decisive factor in the natural slopes dynamics is also crucial.

Landscape structure and hydrographical network knowledge are basis on erosion study. The climate (evaporation, precipitations, …) directly influences the response of a geosystem and erosion phenomena. Soils and erosion features mapping gives major information about runoff and water seepage rates. Knowledge of erosion dynamics increase with aerial and spatial imagery analysis too. Geologists and geographers want to understand connection between soil erosion observed on the terrain and active processes. Development of geographical information systems (GIS) in Earth sciences * Further author information: (Send correspondence to Nazha Selmaoui) Nazha Selmaoui: E-mail: selmaoui@univ-nc.nc, Telephone: +687 26 58 23 Isabelle Rouet: E-mail: isabelle.rouet@univ-nc.nc, Telephone: +687 26 58 23

Remote Sensing of Inland, Coastal, and Oceanic Waters, edited by Robert J. Frouin,Serge Andrefouet, Hiroshi Kawamura, Mervyn J. Lynch, Delu Pan, Trevor Platt,

Proc. of SPIE Vol. 7150, 71501L · © 2008 SPIE · CCC code: 0277-786X/08/$18 · doi: 10.1117/12.804884

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gives new tools to work on maps and DEMs. Working with real or modelized images becomes easier for geologists and geomorphologists. Thematic expert find in these data many information to work on erosion processes. For example, main erosion types, gully erosion or landslides, frequently appears near structures. Origin of these structural link can be relied to geological features (faults, lithology, mechanical properties of rocks…) and to morphology. These two major parameters are inter-dependent, with climatic influence, and shape the landscape. Geological structures are often known and mapped by geologists but linear and planar structures in landscape are less used in erosion studies however the link with erosion is easier to identify. Erosion studies begin with stripped areas mapping, an inventory of relief linear shapes lineaments can be made but rarely proceeded on account of long time analysis. Crossing of this two maps allow to understand the relationship between erosion and landscape linear shapes. In addition, crossing terrain analysis with many environmental data (geology, rains, etc.) allow to predict areas location probably subject to erosion for environmental management or country planning[1] in the global context of sustainable development.

Figure 1 Erosion along a morphological lineament in the ultramafic terrains of New Caledonia

1.2. Why a new method Lineament mapping is usually made by photo-interpretation or by visual analysis on topographical map. Recent research papers show that geologists want to automate lineaments mapping in satellite images ([2]). Landscape modelisation into elevation grids (Digital Elevation Models, DEM) is another alternative and these models allow to work directly on landscape morphology. DEMs seem also to be better basis to perform morphological analysis, there is no stages of pre-analysis like spatial imagery need. However human eye isn't able to directly analyse this greyscale images, and the manual inventory is carried out on hillshades models from DEM. The DEM is lighted up by a potential source of light the incidence direction and the height are not limited like solar lighting. Analysis remains photo-interpretation on this hillshade images (Figure 2). To make a consistent study different lightings must be analysed and this makes the work very long (visual interpretation and digitizing at screen). What analysts manually make finally comes from the same image analysis. We propose in this paper to support morphological analysis with an automatic method for landscape lineaments mapping. Used images are mountainous relief maps obtained by DEM calculations.

2. METHODOLOGY

2.1. Data Data used for DEM calculations are point elevation and contour lines of the 1/10 000 topographical GIS of New-Caledonia ([3]). This grid model is hydrologically correct. Hillshade grid models have been computed in the 8 main geographical directions, always with 45° of incidence. Pixels of DEM data are 10 m x 10 m size, like all hillshades.

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J

Figure 2 Hillshade and DEM images

The interesting zone is a part of a well known geological area where lineaments mapping has been manually made. Results of this preliminary map was realised in a GIS where DEM hillshades are the mapping support (Figure 2). This map is the reference for the validation of automatic analysis.

2.2. Segmentation The segmentation aims to divide image into homogenous regions, by detecting regions or edge of regions. Another approach called watershed, performed on gradient image by detecting crest lines, was developed.

The watershed resulting from mathematical morphology originally proposed by S. Beucher et al.[4] and based on two definitions:

- streaming: a drop of water falling on a relief follows a descending path and eventually reaches a minimum. Watershed lines are the dividing lines of the attraction domains of water drops[5]

- immersion : imagine the local minima are pierced and the relief is immersed in a lake. Catchments basins will fill up and at points where water coming from different basins met, dams are built and considered as watershed lines.

Streaming approach was difficult to implement, immersion one exists under many sequential algorithms([6], [7], [8]) divided into two classes: one based on recursive algorithm and another based on geodesic function. A critical review of watershed algorithms and their associated results can be found in [9]. The major problem is still the oversegmentation. There are many techniques proposed to reduce this oversegmentation. A simple one is the small basins thresholding according to their depth. We also find the combined watershed by immersion to a multiresolution concept [10].

The principle is to detect the more perceptible object at different resolution. In [11] the authors detect the seeds for watershed at different resolution and use them to distinguish significant and non-significant seeds. Another method [12] introducing the graph contraction process was proposed to reduce oversegmentation by processing the plateaus.

We propose in this work, a new alternative of watershed definition close to streaming approach. Accordingly to this point of view, we define an attractive structure between pixels which express the steepest slope path. In this structure, we identify at one step, the minima pixel, pixels along a certain path of steepest slope (associated to a convex regions) and pixels along the valley. The algorithm based on this concept (attraction structure) allows to identify convex region (catchments basins on negative image) and lines. It provides efficiently labelled convex regions and lines. The implementation is simple and the algorithm is fast.

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2.2.1. Principle of the method The principle of this method is to define an attractive structure between pixels on gray level images. All pixel p is associated to a pixel q for which the gray level is the maximum for all upper neighbours of p. The choice of q is associated to a notion of "steepest slope path". We will specify how to define this attractive structure from a function attr. Let I an image and f the gray function.

Definition 1: attr is defined as following :

))()(()(, max)(

pfqfpattrIppVq

−=∈∀∈

(1)

where V(p) is the neighbourhood of p (for example 4 or 8 neighbours).

Figure 3 : Example of tree cases : Free attractor& & Tied attractor & Hanging and tied

Definition 2: Ip∈∀ (Figure 3):

• if attr(p) is negative, then all his neighbours q pixels are such that f(q)<f(p), p is local maximum, p is not "attracted" by any other pixels; p is called then "free attractor".

• if attr(p) is positive, the pixel q0 that realizes the maximum is called "tied attractor" of p; p is "attracted" by q0.

• if attr(p) is 0, let Z the set of pixels realizing this maximum, if it exists Zq ∈0 and q0 not "attracted" by p, then p is "attracted" by q0; else q0 is called "hanging and tied" pixel.

Thus, we superimpose on the image an attractive structure between pixels in which pixel p can be in one of the following situations:

• p is not "attracted" by any other pixel, but "attracts" others; p is a "free attractor".

• p doesn't "attract" any pixels but is "attracted" by others; we say that p is "hanging and tied".

• p is "attracted" by pixels and "attracts" others; we say that p is a "tied attractor".

Theorem 1: So we have:

• "tied and hanging" pixels are pixels belonging to lines.

• "free attractors" and "tied attractors" pixels are pixels on convex regions (catchments basins on image inverse)

2.2.2. Segmentation results We perform our algorithm on one of the hillshade and DEM images (Figure 2). We keep only the lines detected (Figure 4) for hillshade image and catchments basins in DEM (Figure 5). As we see in image result (for hillshade), the lines are thick and some of them cross the same region. We have improved the algorithm by adding a process which refine the thick lines and eliminate the cross ones (see Figure 6).

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Figure 4 lines detection in hillshade and DEM image

Our method is able to detect simultaneously lines and its associated regions (Figure 4 and Figure 5).

Figure 5: Catchments basins on DEM image

As shown in Figure 6, we obtain the thinner lines and all cross lines are eliminated, but some small lines appear. A threshold method of the small lines can be simply performed.

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Figure 6: Thinning lines and eliminating cross lines

2.3. Lines analysis To analyse lines detected by segmentation (see sec 2.2) we use the well-known Hough transform and directions rose diagram method.

2.3.1. Hough transform The Hough transform ([15], [13]), provides a powerful and robust technique to detect geometrical form of a pre-defined shape. This technique is widely used to isolate curves of a given shape in an image. The classical Hough transform [14] requires the curve to be specified in some parametric form. Therefore it is most commonly used to detect regular curves such as lines, circles, and ellipses. We chose this technique because its advantages are the gap tolerance in curves and its robustness to noise. The pixels lying on a curve do not need to be all contiguous. The Hough transform principle is to project the image space into a parameter space that represents the target shape. For a line form, for example, two parameters are unknown and must be estimated.

The line is presented by two parameters in polar coordinates ),( θr , where r is the distance from origin point to line and

θ is the angle of vector supporting r. We define the line { }ryxyxrD =+= θθθ sincos/),(),( , thus the point p(x,y) belong to D if the ryx =+ θθ sincos is true. In the Hough parameters space, the form associated to this is a sinus. To detect lines in image, we must detect the intersection of many sinus, the corresponding parameters ),( θr present the line reached.

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Figure 7: Lines extraction by Hough transform

2.3.2. Rose of directions The rose diagram is a representation of preferential lines direction in image. This diagram plot in each direction, in polar coordinates, the amplitude of all lines in the image. Two methods exist to elaborate this diagram, one based on autocorrelation function and the other on morphological operators.

2.3.2.1. Rose of directions based on autocorrelation function This diagram is based on use of autocorrelation function. Actually, the autocorrelation function [16] brings out the frequency objects in image which expresses the principles orientations of textures. In our case, if we translate on one direction, we get a high correlation.

∑∑+∞

=

+∞

=

++=0' 0'

)','()','(),(k l

xx llkkxlkxlkC (2)

To compute this autocorrelation function, we use the Fourier transform.

2.3.2.2. Rose of directions based on morphological operators The basic idea is to apply a morphological operator (erosion) to eliminate all lines which are not in one direction. We use in this case, a directional structuring element. To perform all directions, we have two possibilities:

- rotate the structuring element in all direction

- rotate the image in all directions and apply the same structuring element.

In the first solution, for a 3x3 structuring element, is to get only four directions. We choose the second solution.

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I

Figure 8: rose diagram

3. CONCLUSION This paper aims to give an approach of test, comparison and improvement algorithms for a lineaments study, first step to an automatic process. It gives also good results for geologist.

We presented a part of process allowing to help geologist to analyse automatically some geomorphologic forms for erosion problem study. We proposed a new segmentation method able to detect lines and regions (catchments basins). The Hough transform can extract lines that are one of geomorphologic forms contributing to soil erosion and are usually faults, joints, or boundaries between geological formations. Other types of lineaments also include roads and railroads.

Finally, the rose diagram gives information about the main direction of eroded form and guide the prediction of areas could be stripped in the future. The autocorrelation function seems a good technique to construct the diagram rose, it can be interesting to extend it to other forms and we can analyse zones where these forms appear and frequently associated to other ones.

As a future work, we plan to assess accuracy of our process by comparing our results to ones manually extracted by geologist. Also, we will complete this process by studying other geomorphologic forms and searching some relationship between them to predict soil erosion.

REFERENCES

[1] Gay, D., Rouet, I., Mangeas M., Dumas P., Selmaoui N., “Assessment of classification methods for soil erosion risks”, Proc. MODSIM 2659-2665 (2007).

[2] Mavrantza, O.,D. and Argialas, D. P., “Object-oriented image analysis for identification of geologic lineaments”, Proc. OBIA http://www.commission4.isprs.org/obia06/papers.htm (2006).

[3] Direction des Infrastructures Terrestres, des Transports et de la Topographie, “Topographical map of New-Caledonia 1/10 000 », Gouvernement de la Nouvelle-Calédonie (2006).

[4] Beucher, S. and Lantuéjoul, C.,”Use of Watersheds in Contour Detection”, Int'l Workshop Image Processing, Real-Time Edge and Motion Detection/Estimation, Rennes, France 17-21(1979).

[5] Serra, J. “Image Analysis and Mathematical Morphologicy”, Academic Press, New York, Tome 1, 610 (1982 ). [6] Meyer, F., “Un algorithme optimal de ligne de partage des eaux“, 8th Congrès Reconnaisance de Formes et

Intelligence Artificielle (RFIA'91), Volume 2, 847-857 (1991). [7] Vincent, L. and Soille, P., “Watersheds in Digital Spaces : An Efficient Algorithm Based on Immersion

Simulations”, IEEE Trans. Pattern Analysis and Machine Intelligence, Volume 13, N°6, 583-598 (1991). [8] Soille, P., “Morphological Image Analysis : Principles and Applications”, Springer Verlag, 391 (2004).

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[9] Roerdink, J.B.T.M. and Meijster, A., “The Watershed Transform : Definitions, Algorithms and Parallelization Strategies”, Fundamenta Informaticae, Volume 41, 187-228 (2001).

[10] Piegay, E., Selmaoui, N. and Leschi, C., “Crest Lines detection by valleys spreading”, Computer Analysis of Images and Patterns, 6th International Conference, CAIP'95, Prague, Czech Republic, September 6-8, LNCS N°970, 270-277 (1995).

[11] Frucci, M., Ramella, G. and Sanniti di Baja, G., “Using resolution pyramids for watershed image segmentation”, J. of Image Vision Comput, Volume 25, N°6, 1021-1031 (2007).

[12] Selmaoui, N., “Agorithm for Crest Detection Based on Graph Contraction”, Pattern Recognition and Image Analysis, Second Iberian Conference, IbPRIA 2005, Estoril, Portugal, June 7-9, Part II, Ed. Jorge S. Marques and Nicolas Pérez de la Blanca and Pedro Pina, LNCS N° 3532, 303-310 (2005).

[13] Duda, R. O. et Hart, P. E.,“Use of the Hough Transformation to Detect Lines and Curves in Pictures”, Comm. ACM, Vol. 15, 11 - 15 (janvier 1972).

[14] Ballard, D.H., “Generalizing the Hough transform to detect arbitrary shapes” Pattern Recognition, vol.13, no.2, 111-122 (1981).

[15] Hough, P.V.C., “Method an means for recognizing complex patterns” U.S. Patent 3,069,654,1962. [16] Bres, S., “Contributions à la quantification des critères de transparence et d’anisotropie par une approche globale”,

PhD Thesis (1994).

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